Quantum graph walks II: Quantum walks on graph coverings
Quantum graph walks II: Quantum walks on graph coverings
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发表时间：
2012-11
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通讯作者：
Y. Higuchi;N. Konno;I. Sato;E. Segawa
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作者：
Y. Higuchi;N. Konno;I. Sato;E. Segawa
给出了量子图G的键散射矩阵的特征多项式的一个新的行列式表达式。给出了G的正则覆盖的键散射矩阵的特征多项式的分解公式。进一步，我们定义了G的L-函数，并给出了它的行列式表达式，作为推论，我们用它的L-函数表示了G的正则覆盖的键散射矩阵的特征多项式.作为应用，我们引入了三种量子图游动，并讨论了它们之间的关系。
We give a new determinant expression for the characteristic polynomial of the bond scattering matrix of a quantum graph G. Also, we give a decomposition formula for the characteristic polynomial of the bond scattering matrix of a regular covering of G. Furthermore, we define an L-function of G, and give a determinant expression of it. As a corollary, we express the characteristic polynomial of the bond scattering matrix of a regular covering of G by means of its L-functions. As an application, we introduce three types of quantum graph walks, and treat their relation.